The Obama administration is to make its strongest declaration yet in support of same-sex marriage, filing an eleventh-hour brief in support of a supreme court challenge to California's law banning such unions.

Advocates for marriage equality have been urging the president to support the two gay couples who are bringing the case, and an administration confirmed on Thursday that it would file a "friend of the court" brief before the deadline at the end of the day.

The case, due to be argued on 26 March, will hear whether California's 2008 law, known as Proposition 8, is constitutional.

Briefs in support of the case have already been filed by a diverse group of Republican and conservative leaders, some of America's leading businesses, 15 states and equality groups.

The Obama administration is not required to file a brief, and earlier indications suggested that he would not, despite speaking in his inaugural last month of gay men and lesbians being treated equally "under the law". Obama has already filed a brief in another, important marriage equality case to be decided by the supreme court, in support of striking down the federal Defense of Marriage Act (Doma) which recognises marriage as only that between a man and a woman. The president supports marriage equality but has said that it should be governed by the states.

The latest case, Hollingsworth V Perry, challenges the constitutionality of Proposition 8, the California law which was enacted in November 2008 and eliminated the right for same sex couples to marry in that state.

Gay marriage advocates are hoping that the Obama administration will file a broad brief in the Prop 8 case, which will argue that not only is the California law unconstitutional but that the constitution forbids any such laws. It could also file a narrower brief, urging judges to strike down only the California law.

Among the companies that have signed a brief supporting the plaintiffs in the case are Apple, Nike, Facebook, Morgan Stanley, Hewlett Packard and Google.

The list of 100 Republicans and conservative signatures of a brief, organized by Former RNC Chairman Ken Mehlman, includes Paul Wolfowitz, former president of the World Bank, Jon Huntsman, former governor of Utah and 2012 presidential hopeful, Beth Myers, former Romney for President campaign manager, Jim Comey, former US deputy attorney general. Some of them have opposed same-sex marriage in the past, including Meg Whitman, the Hewlett Packard CEO, and Huntsman.

In the Doma case, Windsor v United States, a group of almost 300 corporations and employers including Fortune 500 companies have also signed an amicus brief calling for an end to Doma. Both the Doma and the Prop 8 case are due to have oral arguments heard by the court in March.

The broad support for the plaintiffs in both the Windsor and Perry cases is in sharp contrast to the lack of support from businesses for either of the two laws. According to the Respect for Marriage Coalition, no businesses submitted a brief for the other side.

On Thursday, a broad, bipartisan coalition of groups filing briefs in support of marriage equality held a press conference in Washington, where representatives from political, business, labour, health and military groups spoke about their decision to sign a legal document to the court that said so.

"I'm proud to join more than one hundred other Republicans who believe gay Americans shouldn't be excluded from the fundamental right to marry the person you love," said former Republican congressman Jim Kolbe. "As a Republican, I believe in protecting individual freedoms and that everyone – including gay and lesbian Americans – has a constitutional right to be treated equally under the law."

Labour unions said that marriage inequality is bad for employees.

"Working people are standing alongside millions of other Americans in this fight for marriage equality because we believe in fairness and equality and don't think federal or state law should penalize people simply because of who they love," said Valarie Long, executive vice-president of SEIU.

"The court should uphold the court of appeals rulings striking down Doma and Proposition 8 and affirm the fundamental rights of all Americans to recognition of their families."

Military officials and veterans highlighted the inequality Doma brings to military families.

Congressman Patrick Murphy said: "As a military veteran, there is no question that the Defense of Marriage Act, or Doma, discriminates against certain legally married service members, veterans, and their families.

"The impacts of Doma are real and this discriminatory law injures morale, readiness, cohesion and performance. There is no constitutional justification, let alone military rationale, that weighs in favour of permitting these threats to today's military and our national security to continue."

Brian Brown, for the National Organization for Marriage, said there were more than 60 amicus briefs filed in support of Prop 8 and Doma, including from the US Conference of Catholic Bishops, the Family Research Council and the Coalition of African-American Pastors and the Marriage Law Foundation.

"This notion that is central to this whole debate that gay couples and gay individuals are politically powerless is absurd," he said. "They are one of the most organised on Capitol Hill."

Brown said that the brief filed by Nom, in support of Doma, took the opposite view against the plaintiffs argument that the federal government did not have a history of defining marriage.